On a hot spring day, inside a large, airy studio in the town of Castaic, California, a group of men and women are watching paint dry. The occasion is the video shoot for If I Never See Your Face Again by Maroon 5 featuring Rihanna. The concept appears to be high-end erotica. Rihanna and Maroon 5's dashing frontman Adam Levine flirt professionally with each other in a series of smartly furnished sets, one of which has to be repainted between set-ups, hence the drying paint. It neatly sums up the experience of watching a music video being made. As the same song plays over and over again, the hours crumble away, never to return.

If the sets resemble the kind of rooms nobody really lives in, then Rihanna sports a selection of outfits nobody really wears, displaying every inch of the legs that razor brand Venus Breeze insured for $1m last year. After each take, a woman on the crew whoops "Hotness!" or "Smokin'!" Perhaps that her job: sexual chemistry cheerleader. "Her physical presence is undeniable," Levine tells me later, which is a polite way of saying, "Hotness!" It is no slight on Levine, who is a photogenic chap, to say that Rihanna looks as if she could chew him up and spit out the bones.

In between takes, the 20-year-old Bajan is at once friendly and distant. Around this likable woman with a big, bursting "Hya-hya!" laugh, you sense a protective shell of professional detachment - a wary toughness. "When she walked into the office, there was something about her," says Jay-Z, who signed Rihanna to Def Jam four years ago. "She has an intensity and drive for success. I sign artists based on their swagger and level of talent. She's got both."

If you're at all interested in the business of pop, then the emergence of a new star is always intriguing. The phrase "manufactured pop" is misleading, because it implies faultless efficiency. If it were easy to create a star, then the major labels wouldn't be on their uppers. In fact, it's a mysterious confluence of factors: the right voice, face, temperament and song, all coming together at exactly the right time. That's the kind of lightning that struck Rihanna last summer.

Two years ago, Rihanna was just one of many economically named singers - Amerie, Ciara, Cassie - vying for the status of a Beyoncé. Then she got her hands on Umbrella, and it changed her life. Don't pretend you haven't heard it - it was No 1 for 10 weeks last year, during Britain's long, wet summer. Playgrounds and buses resounded to the idiosyncratic hook: "Under my umber-ella-ella-ella. Eh-eh-eh." She has had four more hits since; this week, the acerbic break-up ballad Take a Bow sits at No 2 in the UK charts.

The night before the Maroon 5 shoot, she played LA's Nokia theatre as part of Kanye West's Glow in the Dark tour. Given that West's wildly extravagant headlining set was a cross between 2001: A Space Odyssey, This Is Spinal Tap and a very peculiar dream, she didn't exactly upstage him, but she left her mark. For the Justin Timberlake-penned ballad Rehab, she cradled the microphone, a prop cigarette smouldering between her fingers. During Shut Up and Drive, an electro-rock track based on New Order's Blue Monday, her imperious robo-Amazon bearing recalled Grace Jones.

"I love Grace Jones," she confirms the next day, eating mango chips in her trailer while still wearing her last outfit from the shoot: a very 1980s short black dress and white jacket. She is so flawlessly, unreally beautiful that were it not for the mango chips it would feel like talking to a magazine cover. Her Bajan accent ebbs and flows. When it's strong, "No, actually," becomes "Naw, asherly."

"I never knew of her when I was in Barbados," she continues. "She's just amazing. The things that she did, the things she wore, her fashion, from holding a cigarette to having a flat-top boy haircut. It took a really strong person to do that and as a female I look at her like: You. Are. Amazing. These days a lot of people in the industry wear stuff on stage that they would wear on the street instead of having fun with the fact that you're on stage."

When Rihanna debuted in 2004, much was made of her Bajan heritage. Her album was called Music of the Sun and the single was a hot-weather dance track, Pon de Replay, sung in a thick Caribbean accent. Her second album, A Girl Like Me, was marginally edgier with a song, SOS, built on Soft Cell's Tainted Love, but her image was still cheerfully lightweight.

"When I first started, I didn't know anything," she says. "I didn't really have a say. The second album, I got a little more freedom. That's when I found out what I wanted to do and be but I still wasn't allowed to."

What bothered her most was her haircut. "I felt like the whole world had long, curly, flowy blonde hair," she says in a mockingly cutesy voice. "Ciara, Beyoncé, Mariah, Christina Milian. Everybody wanted to be like everybody else. So I cut my hair and they [Def Jam] made me put my long hair back in [as extensions]. The second time, I didn't have any discussions, nothing. I just cut it, I dyed it black, I went into the studio making music my way. I found myself all at once. I like things strong, edgy, a little to the left. I don't like things that are expected - nothing cliched."

Umbrella was, therefore, the perfect song for her: addictive but ominous, strong but playful, sexy but subtly so, a synth-rock power ballad in urban clothing. Terius "The Dream" Nash and Christopher "Tricky" Stewart wrote it in a matter of hours in January 2007, then shopped it around to Mary J Blige and Britney Spears as well as Rihanna. She was not best pleased.

"No one wants to be teased," she says sternly. "How can you bring a record to me when you took it to a million people at the same time? I thought Mary J Blige was going to get it for sure. But at the back of my mind I was thinking, No wait, I'm never giving this up. I went up to the guy [Nash] at the Grammys and I was like, 'Umbrella is my.' And he just kind of giggled. And I really held his face" - she grabs her own jaw to demonstrate - "like, 'No you're not hearing me, Umbrella is my record.'"

You can believe it. It's the commanding certainty beneath Rihanna's charm that makes Umbrella work. Mary J Blige would have overplayed it. Britney Spears would have had a hard job selling the idea that she was anybody's tower of strength. Rihanna has the right blend of sweetness and steeliness.

"[Tricky] said he was still unsure whether Rihanna was the right choice for the song," says Nash, "but when she recorded the 'ellas', you knew it was about to be the jump-off. Your life was about to change if you had anything to do with that record."

"I never knew that this song was going to be so big," says Rihanna. "And I still can't really fathom how big it blew up to become, in places all over this world that I've never heard of. I couldn't really get a hold of that. To this day it never gets old. It's a magical song to me."

Umbrella went to No 1 in 17 countries and has been covered by everyone from Mandy Moore to the Manic Street Preachers. Rihanna performed a version at the Brit awards with a visibly refreshed Klaxons. "Whoo!" she exclaims. "I love the version with the Klaxons. Because the song that we mashed it with is actually a song that I love."

Growing up in Barbados, Robyn Rihanna Fenty subsisted on a high-sugar diet of melodramatic balladeering - Whitney, Celine, Mariah - and aspired to do the same. "I had every confidence this was going to happen. Maybe I was just dreaming, but it's actually coming true."

Pushed to come up with a plan B, she says maybe she would have tried psychology. "I have always been the one that my friends come to for advice. Being able to read people very well helps me in this business for sure, because there are a lot of fake people. Everything that people say to me, I always know it can be a lie. I know that people say things because they think I'm stupid. So now I ask a lot of questions. I like to do my research."

It was a lively household, with people always coming and going: "Friends or family or just people who didn't have any place to stay. My mom was like the big mother." Mrs Fenty sounds like a formidable character. "My mom always told me never to lower my standards for anyone or anything," Rihanna says firmly.

So when Rihanna's dad became addicted to crack cocaine, he got short shrift, and Rihanna had to help raise her two younger brothers. "I was always mature for my years because of the parental part of it." Although her dad has since recovered, his experience has left her unlikely to "do a Winehouse".

"Because I've seen up close what effect those things can have on someone, I would never want to put myself in that situation. It would be very careless and just not smart at all." When she's talking about issues of control, her jaw tightens and juts out in a caricaturist's representation of resolve. She doesn't seem to realise she's doing it.

When she was 15, Rihanna won both a school beauty contest and the attention of a holidaying record producer, Evan Rogers, who signed her to his company and introduced her to Def Jam's Jay-Z and LA Reid. She lives in LA now. "I miss the beaches, I miss the weather, I miss the food. America is a different kind of pace."

Back in Barbados, there are babies called Rihanna in her honour. The day after her 20th birthday in February, she attended the island's first Rihanna Day, where she was greeted at the airport by the prime minister and serenaded on stage by local artists singing her hits. She still sounds slightly bewildered by the whole thing. "I couldn't believe it was happening because I was looking at my friends in the crowd and thinking, 'Oh my gosh, this was something we all would have come to together. And now they're all coming in honour of me.' It was a little strange. But it was awesome."

For now, Rihanna is still young enough not to have been shaped and hardened by the industry. After a few years in the spotlight, most singers develop either the guarded charm of a Kylie or the mad, cosseted narcissism of a J-Lo. "People really thought I was going to get out of my head and become some super diva chick. And to this day that never happened. I don't ask for extravagant things like flowers flown in, or the room to be all one colour."

But the level of work required to be a rising star does not lend itself to a normal life. When I speak to her on the phone a week after our first meeting, we talk about her schedule. "As a new artist they really work the living daylights out of you. Oh my goodness! It's not like my work got easier - it just got manageable."

I ask her what she did on her last day off. She considers it an odd question. "I shot a video. The one you were at."

No, I mean your last day off from work. "Um." There's silence on the line.

"Can't remember. Probably just slept."

When and where are you most relaxed? "Um, I love being on my tour bus. It's very cosy and there's a lot of fun stuff to do. And I get to sleep a lot."

Do you have any hidden talents that have nothing to do with your work? "Nope." Is that because you've devoted all your energies to becoming a singer? She makes a curious croaking sound, which could be either a laugh or a sigh. "Well, I don't have a choice."

The album, Good Girl Gone Bad, is reissued on Def Jam on June 2. The single, Take a Bow, is out now